Chapter EP, Problem 12.3.1EP

To determine

To find: The probability of the student.

Answer to Problem 12.3.1EP

The probability of the student is $0.288$ .

Explanation of Solution

Given information:

The given table is,

Explains well; Easy tests

Explains well; Hard tests

Explains poorly; easy tests

Explain poorly; Hard tests

Junior	59	63	52	31
Senior	61	47	79	26

Calculation:

Consider the student’s junior is event $A$ and event $B$ that the students rates the teacher as explain well.

Total number of students is $418$ .

Number of junior are $205$ and number of senior is $213$ .

Calculate the probability.

  $\begin{array}{c}P\left(A\right)=\frac{205}{418}\\ P\left(AandB\right)=\frac{59}{418}\end{array}$

  $\begin{array}{c}P\left(A/B\right)=\frac{P\left(AandB\right)}{P\left(A\right)}\\ =\frac{\frac{59}{418}}{\frac{205}{418}}\\ \approx 0.288\end{array}$

Therefore, the probability of the student is $0.288$ .